The only sport really split in Ireland between Ireland and Northern Ireland is soccer where there are two national teams and leagues. Even then anyone from the North can play for the 'Republic' team (and vice versa but nobody has or ever will you'd imagine).
Ireland's Call was commissioned for rugby and sung at home games after Amhrán na bhFiann and sang away from home as the sole anthem. The Irish cricket team have used it in an unofficial fashion for a few years too I think. At the Rugby World Cup the tricolour and the flag of Ulster was used to represent Ireland. At the Golf World cup we had just the tri colour though (which is funny as Rory McIlroy and Graham McDowell, both from the North, were the representatives). I'd favour Ireland's Call and a new Ireland sports flag to be used for all of our sports. Get rid of the confusion.
The Yank flag makes no sense. Irish Americans like shamrocks and the tri colour.